ode45 with two 2nd order differential equation
13 views (last 30 days)
Show older comments
![1.PNG](https://www.mathworks.com/matlabcentral/answers/uploaded_files/218945/1.png)
Here I have two differential equations and I want to solve it using ode45
![2.PNG](https://www.mathworks.com/matlabcentral/answers/uploaded_files/218946/2.png)
I am asked to convert the two 2nd order equations to 4 first-order equations which are suitable for ode45.
0 Comments
Answers (5)
Steven Lord
on 11 May 2019
See the Higher-Order ODEs example on this documentation page and use the technique it illustrates to turn your system of two second order ODEs into a system of four first order ODEs.
0 Comments
Pulkit Gahlot
on 19 May 2020
'first make the function file'
function xval = pulfun(t,y)
%constant
u=0.012277471;
%define dy/dt
xval(1,1)=y(3);
xval(2,1)=y(4);
xval(3,1)=y(1)+2*y(4)-(1-u)*(y(1)+u)/((y(1)+u)^2+y(2)^2)^(1.5)-u*(y(1)-1+u)/((y(1)-1+u)^2+y(2)^2)^(1.5);
xval(4,1)=y(2)-2*y(3)-(1-u)*y(2)/((y(1)+u)^2+y(2)^2)^(1.5)-u*(y(2))/((y(1)-1+u)^2+y(2)^2)^(1.5);
end
'(then write a script file for use of ode45)'
y0=[0.994;0;0;-2.00158];
tspan=[10 40];
[tsol,ysol]=ode45(@(t,y) pulfun(t,y),tspan,y0);
plot(tsol,ysol)
i used my own terms. You can use your.
1 Comment
Stephane Sarrete
on 21 Nov 2020
Hello,
Please, I don't understand what the y (1), y (2), y (3) and y (4) represent in the function definition. Can be stupid question but I really do not understand. Thank you for helping me.
1 Comment
Stephan
on 21 Nov 2020
Since 2 ode of order 2 are transformed into 4 ode of order 1, the 4 different entries of the y-vector represent the 4 four unknowns, to solve for.
See Also
Categories
Find more on Ordinary Differential Equations in Help Center and File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!